Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
344 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22612134 | C2 | semidirect |
| 3. #22612131 | C2 | semidirect |
| 5. #22607942 | C2 | semidirect |
| 7. C73×#1348 | C2 | semidirect |
| 169. #1348 | D73 | semidirect |
| 171. C73 | #12282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620702 | 2 |
| #22612134 | 2 |
| #22612131 | 2 |
| #22611361 | 2 |
| #22607942 | 2 |
| #22607854 | 2 |
| C73×#1348 | 2 |
| #12282 | 73 |